Date of Award
6-26-2026
Date Published
July 2026
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Physics
Advisor(s)
Christian Santangelo
Keywords
Curvature propulsion;Droplet pinch-off;Elasticity;Fluid mechanics;Soft matter physics
Subject Categories
Physical Sciences and Mathematics | Physics
Abstract
This dissertation examines two disparate problems in soft matter physics that are connected by a shared objective– employing geometry as a mechanism for controlling them. In the first problem, we consider strategies for navigation on frictionless curved surfaces. Inspired by meniscus-climbing insects, we envision a curvotactic device–a “surfer”– capable of navigating a curved surface by tuning its geometry. The surfer is constructed from narrow strips and their curvature mismatch with the confining surface provides the necessary net forces and torques for motion. Manipulating the surfer’s geometry then tunes this response to curvature. Further, we detail the pivotal role played by umbilical points of two-dimensional surfaces. They enable strong and predictable entrapment of the surfer in their neighborhood, while also coupling the surfer’s absolute orientation with its position. Using the umbilics of a surface as geometrical landmarks, these effects allow a surfer to deliver itself to desired locations on arbitrary curved surfaces. In the second problem, we study the splitting of a droplet held between the tips of fibers. We describe a sharp transition in the post-rupture state that is governed by the angle between the fibers. We ascribe this transition to the nature of the bifurcation at the point of collapse. A perturbation analysis then predicts this threshold angle and we find that it is, surprisingly, independent of fluid properties, depending solely on the fibers’ geometry. We then observe, via experiments, that the depinning of the droplet’s contact line enhances the asymmetry in the post-rupture volume distribution, enabling a near-complete transfer of a droplet. We leverage this response in a device that uses a ruck to pass a droplet along a train of fibers, a proof-of-concept for the geometric control of droplets. Despite their differences, these problems demonstrate how geometry can permeate even commonplace physics and how uncovering these connections can be surprisingly complicated, yet fun.
Access
Open Access
Recommended Citation
Hulikal Narasimhamurthy, Samay, "Surfing Shapes and Breaking Bridges: Geometric Control in Soft Matter" (2026). Dissertations - ALL. 2325.
https://surface.syr.edu/etd/2325
